1. Field of the Invention
The present invention relates to computer-readable recording medium for recording a mask data generation program, a mask data generation method, a mask fabrication method, an exposure method, and a device manufacturing method.
2. Description of the Related Art
There has conventionally been used a projection exposure apparatus, which causes a projection optical system to transfer a circuit pattern drawn on a mask (reticle) onto a substrate (e.g., a wafer). Under the circumstances, a demand for a high-resolution exposure apparatus is increasing. Known high-resolution exposure methods increase the numerical aperture (NA) of a projection optical system, shorten the exposure wavelength (λ), or decrease the k1 factor.
Circuit patterns are roughly classified into interconnection patterns (line patterns) and contact hole patterns. Generally speaking, it is more difficult to expose fine contact hole patterns than fine line patterns.
Various improvements in exposure techniques are being attempted, to form fine contact hole patterns by exposure. A representative technique inserts an auxiliary pattern that is not resolvable in a mask on which a contact hole pattern to be transferred is drawn. This is one approach to decreasing the k1 factor.
Japanese Patent Laid-Open Nos. 2004-221594 and 2005-138981 have described techniques of deriving, by numerical calculation, how to insert an auxiliary pattern. According to these techniques, an approximate distribution of imaging plane amplitude is obtained by numerical calculation to derive an interference map. That is, the interference map expresses an approximate distribution of imaging plane amplitude.
More specifically, a transmission cross coefficient (to be referred to as a TCC hereafter) is derived. An aerial image undergoes decomposition (singular value decomposition; SVD) into N images (called eigenfunctions, N: a natural number) on the basis of the TCC result. This method is called a sum of coherent system decomposition (to be referred to as SOCS hereafter).
The N eigenfunctions decomposited by SOCS each have a positive or a negative value. An eigenvalue (ith eigenvalue) corresponding to the ith eigenfunction is multiplied by the square of the absolute value of the ith eigenfunction to obtain N functions. The N functions are added to obtain an aerial image.
Assuming that a largest eigenvalue is the first eigenvalue and its corresponding eigenfunction is the first eigenfunction, the first eigenfunction most contributes to forming an aerial image. In view of this, the aerial image is approximated by the first eigenfunction. This approximation allows the derivation of an imaging plane amplitude distribution. That is, an interference map can be calculated.
An auxiliary pattern is inserted in a portion having a positive value in the interference map, such that exposure light transmitted through the contact hole pattern is in phase with that transmitted through the auxiliary pattern. An auxiliary pattern is inserted in a portion having a negative value in the interference map, such that the phase difference between exposure light transmitted through the contact hole pattern and that transmitted through the auxiliary pattern is 180°.
Unfortunately, the techniques described in Japanese Patent Laid-Open Nos. 2004-221594 and 2005-183981 require the calculation of a TCC and eigenfunction to derive an interference map. This often complicates the whole numerical calculation, to result in a long mask data generation time.